The invention relates to digital data processing and, particularly, to novel methods and apparatus for forward-projection and back-projection for use, e.g., in reconstructive imaging. The invention has application in health care and, specifically, medical imaging—as well as in a host of other areas, such as manufacturing, security, research, and defense.
A forward-projection is an operation for estimating the (two-dimensional) transmission or emission shadow that would result from illumination of a (three-dimensional) object by a point source which emits radiation that partially passes through the object. By way of example, a forward-projection could be performed in order to provide an estimate of what an x-ray image of a human might look like. The term forward-projection also refers to the estimate that is determined from executing a forward-projection operation.
A back-projection is an operation for generating a simple estimate of the structure of a (three-dimensional) object that could produce a given (two-dimensional) transmission or emission shadow, if that object was illuminated by a point source which emits radiation that at least partially passes through the object. To continue the example, a back-projection could be performed in order to generate a simple estimate of the body structures the imaging of which resulted in a particular x-ray image. As above, the term back-projection also refers to the estimate that is determined from executing such a back-projection operation.
Reconstructive imaging is a procedure for constructing a three dimensional (3D) model of a subject from a series of two-dimensional (2D) projection images. These projection images are typically generated by exposing the subject to a x-ray (or other radiation) point source that is positioned on one side of the subject and measuring the transmitted (or non-absorbed) radiation with a 2D detector that is positioned on the opposite side of the subject. A series of these projections is created by repeatedly measuring the transmitted radiation as the point source and/or the detector are moved differing locations relative to the subject.
For example, computed axial tomography (CAT) is a reconstructive imaging technique in which a three-dimensional model of the internals of an object—typically, some portion of the human body—is constructed from a series of two-dimensional x-ray projections taken at evenly spaced angles that surround the object. With the aid of a computer, the series of acquired 2D projection images are computationally projected backwards to estimate the relative density of the internal structures of the object (e.g., in the case of a head, the skull, gray matter and other resolvable structures). While no one of these back-projections is, by itself, sufficient to identify those structures, the computational combination of all of the back-projections typically produces a reasonable 3D representation of the object. Because this typically involves performing back-projections on hundreds, if not thousands, of projected images, reconstruction systems typically incorporate special-purpose hardware in order to provide timely results. Though prior art solutions have proven effective in this regard, they are typically quite expensive.
Moreover, those prior art solutions for determining back-projections have limited applicability to a new class of imaging, referred to as tomosynthesis, in which a relatively small number of projection images are acquired from only a limited number of x-ray source positions (or foci). Typically, these foci are distributed across a limited arc. For this type of imaging, the requisite reconstruction requires an iterative approach. In these systems, the computations include not only back-projections, but also forward-projections, in which estimates of the volume being reconstructed are projected “forward” to generate hypothetical projection images for computational comparison with actual measured projection images acquired by the imaging equipment. By comparing the hypothetical forward projection of the current 3D model to the measured projection images, a correction image can be calculated and used to update (modify) the current 3D model.
CAT scanners and tomosynthesis systems are not the only medical imaging equipment that use forward-projections and/or back-projections. Forward-projection and back-projection operations also form the basis of a broader class of computer-based imaging techniques, referred to as computed tomography (CT), as well positron emission tomography (PET), single photon emission computed tomography (SPECT), to name but a few. In addition, back-projection and forward-projection are used outside the medical field, for example, in manufacturing (e.g., to inspect articles for defects), security (such as baggage scanning) in research, defense and so forth.
An object of the invention is to provide improved digital data processing apparatus and methods. Another object is to provide such apparatus and methods as can be applied in reconstructive imaging applications, e.g., of the types referred to above (by way of non-limiting example).
Related objects of the invention are to provide such apparatus and methods as can be performed more rapidly and with fewer computational resources. A related object of the invention is to provide such methods and apparatus as can be performed with less expensive equipment, off-the-shelf or otherwise.